Given the following history, use a three-quarter moving average to forecast the demand for the third quarter of this year. Note: the 1st quarter is January, February, and March; 2nd quarter April, May, June; 3rd quarter July, August, September; and 4th quarter October, November, December.

 	JANUARY	FEBRUARY	MARCH	APRIL	MAY	JUNE	JULY	AUGUST	SEPTEMBER	OCTOBER	NOVEMBER	DECEMBER
Last year	125	140	150	190	200	225	165	155	145	225	250	275
This year	140	150	170	205	230	260	0	0	0	0	0	0


To forecast the demand for the third quarter of this year using a three-quarter moving average, we’ll average the demand over the previous three quarters (using last year’s data and this year’s data available so far).

Here's how to calculate the moving average:

1. **First Quarter Moving Average**:
   \[
   \text{(125 + 140 + 150) / 3} = 138.33
   \]

2. **Second Quarter Moving Average**:
   \[
   \text{(190 + 200 + 225) / 3} = 205
   \]

3. **Third Quarter Moving Average**:
   \[
   \text{(165 + 155 + 145) / 3} = 155
   \]

4. **Fourth Quarter Moving Average**:
   \[
   \text{(225 + 250 + 275) / 3} = 250
   \]

Using these values, we now calculate the three-quarter moving average up to the third quarter of this year. We’ll average the first three quarters of the previous year to get the forecast for the third quarter of this year.

### Three-Quarter Moving Average (for the Third Quarter of This Year)
Using last year's averages from Q1, Q2, and Q3:
\[
\text{(138.33 + 205 + 155) / 3} = 166.11
\]

**Forecasted demand for the third quarter of this year** is approximately **166** units (rounded to the nearest whole number).

Would you like more details on any part of this calculation?

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Here are some related questions to deepen understanding:

1. How would the forecast change if we used a four-quarter moving average instead?
2. What if demand increases significantly in the second quarter—how would this impact the forecast for the third quarter?
3. How does using a weighted moving average differ from a simple moving average in forecasting?
4. Why might a three-quarter moving average be chosen over a two- or four-quarter moving average?
5. How could seasonality affect forecasts in quarterly data?

**Tip:** Always double-check which quarters are included in the moving average, as errors here can impact forecast accuracy.

Given the following history, use a three-quarter moving average to forecast the demand for the third quarter of this year. Note: the 1st quarter is January, February, and March; 2nd quarter April, May, June; 3rd quarter July, August, September; and 4th quarter October, November, December.

JANUARY FEBRUARY MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER OCTOBER NOVEMBER DECEMBER
Last year 125 140 150 190 200 225 165 155 145 225 250 275
This year 140 150 170 205 230 260 0 0 0 0 0 0

Calculate the forecasted demand for the third quarter using a three-quarter moving average based on historical quarterly data. This guide explains the step-by-step approach, covering key time series analysis concepts and moving average calculations. Ideal for students in Grades 10-12.

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